Religious Typology Quiz

Pythagorean theorem

But was the Pythagorean Theorem derived by pure reason?

My feeling is that Pythagoras saw triangles and attempted to understand the behavior of those triangles (he apparently had more than just a "friendship" with shapes and geometry). As such I assume he rather derived the theorem from observation....and dare I say measurement.
 
Observation, in and of itself, isn't a synonym for empiricism. Empiricism is the derivation of knowledge from a collection of particulars. Deduction or rationality is the derivation of knowledge from first principles or self evident truths.

Aristotle's theory of logic was almost entirely based on deduction.

The Pythagorean theorem was a deduction.

Einstein's thought experiments about gravity and fields of acceleration were famously deductive rather than empirical.

Utilitarian moral theory is a deduction.

OTOH, I would say Darwin's theory of evolution by natural selection was empirical in it's approach

I don't think deduction, per se, is necessarily an epistemology. It is a part of epistemology, the "justification" of the premise.

To say that the pythagorean theorem was "deduced" is to ignore the fact that triangles were observable and measurable and likely physically led to the development of the theorem.
 
Yes, inductive experimentation is the essence of science.

But like I've been saying, not everything in the human experience is amenable to laboratory experiments or mathmatical analysis: freedom, justice, equality, etc.

The reason we tend to get confused as to the nature of knowledge, deduction, and induction is it doesn't get taught at school anymore. Formal logic has entirely dropped out of our educational system, and unless one actually reads the theorems in a high school geometry textbook, one never actually gets exposed to formal deductive logic.

The Anglo-American intellectual tradition at least since Francis Bacon has placed induction and empiricism in the forefront, while on the continent they sort of held on to deduction and rationality as modes of knowledge.

Agreed that all are valid tools and should be used appropriately when able. Why someone would completely disregard a tool is a mystery to me.
 
Yes, inductive experimentation is the essence of science.

But like I've been saying, not everything in the human experience is amenable to laboratory experiments or mathmatical analysis: freedom, justice, equality, etc.

The reason we tend to get confused as to the nature of knowledge, deduction, and induction is it doesn't get taught at school anymore. Formal logic has entirely dropped out of our educational system, and unless one actually reads the theorems in a high school geometry textbook, one never actually gets exposed to formal deductive logic.

The Anglo-American intellectual tradition at least since Francis Bacon has placed induction and empiricism in the forefront, while on the continent they sort of held on to deduction and rationality as modes of knowledge.

The most famous deduction of all, at least as an American citizen, is Thomas Jefferson's formulation of self evident truths about equality and natural rights as the basis to justify American independence.
 
I believe that is indeed the point the other poster was trying to make.

That makes knowledge a posteriori as opposed to a priori.

Knowledge can be both. However, we often use empirical evidence to confirm deductions, but it's not always required.

Again, it's important to use all tools available and to select the best tool for the job. I fail to see why some here are arguing that one or the other is lesser or should be ignored.
 
I don't think deduction, per se, is necessarily an epistemology. It is a part of epistemology, the "justification" of the premise.

To say that the pythagorean theorem was "deduced" is to ignore the fact that triangles were observable and measurable and likely physically led to the development of the theorem.

Deduction does not have to happen in the absence of observation. The key formulation of deduction is knowledge derived from self evident truths. The Babylonians realized there were self evident truths about spatial relationships that led them to deduce a universal truth valid for all time about right triangles.

Aristotle's deductive logic syllogisms fabulously involve observation of self evident truths and first principles.

All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.

^^deduction
 
We hold hold as self evident truths that men are created equal and endowed by their Creator with certain inalienable rights, including life and liberty.

^^ This is a deductive formulation used in justifying the independence of the United States
 
The most famous deduction of all, at least as an American citizen, is Thomas Jefferson's formulation of self evident truths about equality and natural rights as the basis to justify American independence.

Interesting conjecture. I will counter by saying that there is clearly no such thing. Even Jefferson himself knew this since he owned slaves and had relations with one of them for a very long time. It was in no way "self-evident" to him but he could quite plainly see that the offspring from his relationship with a slave were fully human, yet this did not move him sufficient to infer that Sally Hemmings was, herself, a human and as such would be able to enjoy those "self evident" rights which he chose to deny her and his other slaves.

But further: do you think that all animals have a sense of justice and fairness? They would have to if these things are universal. If they ONLY apply to people, well, then you have your answer: they are concepts which WE decided should be put in place. Not some self-evident truth that transcends all of nature.

If I can explain the existence of "fairness" in terms of psychology and biology and evolutionary theory why would I then need to hypothesize that these things are somehow beyond the physical world or require abstract pure reason?
 
Interesting conjecture. I will counter by saying that there is clearly no such thing. Even Jefferson himself knew this since he owned slaves and had relations with one of them for a very long time. It was in no way "self-evident" to him but he could quite plainly see that the offspring from his relationship with a slave were fully human, yet this did not move him sufficient to infer that Sally Hemmings was, herself, a human and as such would be able to enjoy those "self evident" rights which he chose to deny her and his other slaves.

But further: do you think that all animals have a sense of justice and fairness? They would have to if these things are universal. If they ONLY apply to people, well, then you have your answer: they are concepts which WE decided should be put in place. Not some self-evident truth that transcends all of nature.

If I can explain the existence of "fairness" in terms of psychology and biology and evolutionary theory why would I then need to hypothesize that these things are somehow beyond the physical world or require abstract pure reason?

I didn't ask you to accept Jefferson's formulation as true.

I have multiple posts on this thread questioning the frequency we actually aquire true, universal, and certain knowledge which cannot be doubted.

I employed Jefferson's and Aristotle's formulations as a demonstration of deductive reasoning that has been used by moral philosophers, theologians, mathmeticians, historians for thousands of years when scientific experimentation and sensory perception are not effective avenues of acquiring knowledge.

I have never seen a legitimate body of peer reviewed scientific work that claims freedom, equality, and justice are universal biological laws easily explained by equations and laboratory experiments.
 
I didn't ask you to accept Jefferson's formulation as true.

That's an interesting approach. You provided it as an example of something we have knowledge of through pure reason.

I employed Jefferson's and Aristotle's formulations as a demonstration of deductive reasoning that has been used by moral philosophers, theologians, mathmeticians, historians for thousands of years when scientific experimentation and sensory perception are not effective avenues of acquiring knowledge.

And I think I laid out a reason to doubt that the example of the "self-evident truths" are, indeed, anything but "self-evident" or even "truths" in a universal sense.
 
Last edited:
We hold hold as self evident truths that men are created equal and endowed by their Creator with certain inalienable rights, including life and liberty.

^^ This is a deductive formulation used in justifying the independence of the United States

No, it is a rhetorical flourish that even the writers themselves didn't believe or understand.
 
Knowledge can be both. However, we often use empirical evidence to confirm deductions, but it's not always required.

Again, it's important to use all tools available and to select the best tool for the job. I fail to see why some here are arguing that one or the other is lesser or should be ignored.

And certain kinds of knowledge cannot be derived by use of experimentation and the scientific inductive method.

People can't actually agree on what freedom and equality means, or if it's even a good thing. Karl Marx, Plato, Thomas Jefferson, Jesus, and Thomas Hobbes would all have very different conceptions of the nature of freedom and equality.
 
Observation



Observation



Yes, that is deduced but solely because a thing is what it is and not some other thing. 1=2-1.

In this case we aren't really "learning anything", we are merely classifying things based on observation and the concept that a thing is what it is and not some other thing.

You're making the mistake of assuming that empiricism is a synonym for observation.

https://www.justplainpolitics.com/s...Religious-Typology-Quiz&p=5496635#post5496635

I gave examples on this thread of deductions that did not require sensory perception and experimentation. I'm not interested in belaboring the point by listing even more.
 
You're making the mistake of assuming that empiricism is a synonym for observation.

Actually believe I attempted to discuss that exact point here:

I don't think deduction, per se, is necessarily an epistemology. It is a part of epistemology, the "justification" of the premise.

I gave examples on this thread of deductions that did not require sensory perception and experimentation. I'm not interested in belaboring the point by listing even more.

I saw your lists and attempted to address them. You are in no way required to provide more lists, but perhaps engaging on the points I raised about items on those lists might be more fruitful.
 
Last edited:
And certain kinds of knowledge cannot be derived by use of experimentation and the scientific inductive method.

What about if someone does? Is it simply ignored so that the original contention can be maintained?

People can't actually agree on what freedom and equality means

That would then indicate there is not universality to the concept. I don't personally believe that, but my version of "universality" is not quite the same I sense. But if no one can really agree on something does it count as something we "know" and hence as a result of a solid epistemology?
 
What about if someone does? Is it simply ignored so that the original contention can be maintained?



That would then indicate there is not universality to the concept. I don't personally believe that, but my version of "universality" is not quite the same I sense. But if no one can really agree on something does it count as something we "know" and hence as a result of a solid epistemology?

Claims that someday someone might experimentally derive a mathmatical equation for the nature of justice freedom and equality is not a convincing argument, and I do not find it profitable to speculate about hypothetical events in the future.

Universal and certain knowledge is a rare and precious commodity to find in any intellectual endeavor, scientific or not. Newton thought he had discovered a certain and universal law, but it turns out his assumptions were flawed.

Kant's theory of categorical moral imperatives was a form of deductive knowledge which did not require experiments or sensory inputs. A couple of posters have asked me to identify deductive knowledge independent of empiricism, and that is the last one I am going to identify in a running list of them I have given.
 
Here's a wrinkle. Let's talk about "Fairness" for a moment. If "fairness" is only understandable through pure reason then one must assume that our dogs are conducting pure reason:

Dogs Understand Fairness, Get Jealous, Study Finds

A PNAS published study finds evidence that "...[d]ogs have an intuitive understanding of fair play and become resentful if they feel that another dog is getting a better deal, a new study has found."

This actually supports my position that "fairness" is an important biological feature of social animals. It can be explained by its necessity from a purely physical standpoint without any extensive philosophy required. Fairness stabilizes social networks and social networks provide an evolutionary advantage to animals like dogs and humans.
 
Claims that someday someone might experimentally derive a mathmatical equation for the nature of justice freedom and equality is not a convincing argument, and I do not find it profitable to speculate about hypothetical events in the future.

Universal and certain knowledge is a rare and precious commodity to find in any intellectual endeavor, scientific or not. Newton thought he had discovered a certain and universal law, but it turns out his assumptions were flawed.

Kant's theory of categorical moral imperatives was a form of deductive knowledge which did not require experiments or sensory inputs. A couple of posters have asked me to identify deductive knowledge independent of empiricism, and that is the last one I am going to identify in a running list of them I have given.

And the lists are great. Really appreciated which is why I like to leverage the contents of those lists to attempt to make a point. It appears that my points are so valueless as to not even require any engagement other than to remind me that lists have already been supplied QED.

This doesn't feel like a philosophical discussion right now. Alternatives are not entertained and are simply ignored.
 
Back
Top